地磁场空间延拓方法研究

发布时间：2018-04-10 16:35

本文选题：地磁场延拓 + 积分半径　；参考：《山东农业大学》2015年硕士论文

【摘要】：地磁场作为一个天然地球物理场蕴含着大量有用信息。对于物探来说,磁异常数据是一个敏感的指示信号,因此,磁法探测以其成本低、效率高、地域限制小及信息量丰富的特点成为最古老的一种物探方法,而地磁场的空间延拓对于磁测数据资料的解译与分析起着重要作用,很早就成为物探工作者的研究热点,但其对延拓精度要求不高。随着导航技术的不断创新和发展,地磁场作为一个天然的坐标系逐渐成为导航领域研究新对象,对于地磁匹配导航来说,空间地磁数据库的建立同样离不开地磁场延拓,并且对地磁场的空间延拓精度提出了更高的要求。地磁场空间向上延拓属于定解问题,在数学上可以通过求解边界积分方程得到十分精确的延拓结果,但向下延拓属于不适定问题,无法像向上延拓那样直接求解边界积分方程得到稳定的延拓结果。本文以地磁导航应用需求为出发点,以空间地磁数据库的建立为目标,对地磁场空间延拓理论进行了研究,并在此基础上研究了地磁场空间延拓积分半径对延拓结果的影响以及频率域地磁场向下延拓方法。主要研究成果和创新点概括如下:(1)简单介绍了地磁场七要素及其之间的相互关系、地磁场的组成以及各组成部分的特征规律;详细论述了地磁场延拓的数学原理并对空间域向上延拓的积分公式进行了推导,在此基础上推导了频率域原始向上与向下延拓算子;阐述了频率域地磁场向上和向下延拓的基本流程。(2)借助单位脉冲函数研究了地磁场延拓的积分半径大小对延拓结果的影响,分析了不同积分半径内磁测数据对延拓结果的贡献率,研究结果为地磁场向上、向下延拓积分半径的确定提供了参考。(3)在总结了前人对迭代向下延拓法研究成果的基础上,对频率域迭代向下延拓方法进行了更一般推广,给出了频率域迭代向下延拓的一般的公式,并对得到的迭代法向下延拓算子(,)n x yH k k的收敛条件、滤波特性进行了研究和分析。实验结果表明:频率域迭代法向下延拓算子本质上属于一个半收敛滤波算子,迭代次数在一定范围内时,相对原始向下延拓算子有较好的压制高频的作用,从而得到稳定的下延结果,但随着迭代次数的不断增加,迭代算子会越来越逼近原始向下延拓算子,从而使延拓结果又重新变的发散。因此,选择适当的迭代次数十分关键。(4)对不适定问题的性质及其正则化解法的原理进行了研究,详细分析了目前在地磁场向下延拓问题中应用较多的频率域向下延拓Tikhonov正则化方法;针对频率域向下延拓Tikhonov正则化算子过渡频带较宽的问题提出了改进方法,构建了改进正则化算子;对目前确定正则化参数的L曲线法进行了简化,构造出了确定正则化参数的辅助函数;利用海洋实测数据对地磁场空间向下延拓的Tikhonov正则化方法和改进的向下延拓正则化方法进行了实验对比分析。结果表明,向下延拓的Tikhonov正则化方法和改进正则化方法都对含有噪声的磁测数据均具有较强的抗干扰能力,且改进的向下延拓正则化方法较Tikhonov正则化方法具有更高的延拓精度。
[Abstract]:The magnetic field as a natural geophysical field contains lots of useful information for geophysical prospecting, magnetic anomaly data is a sensitive indication signal, therefore, magnetic detection with its low cost, high efficiency, small features rich geographical restrictions and the amount of information has become a kind of geophysical exploration method, the oldest, and geomagnetic field the space extension for the interpretation and analysis of magnetic data plays an important role in the early geophysical workers become the focus of research, but its continuation accuracy is not high. With the continuous innovation and the development of navigation technology, the magnetic field as a natural coordinate system has gradually become a new research object navigation field. For geomagnetic matching navigation, a space geomagnetic database also cannot do without the magnetic field extension, and the magnetic field space extension precision put forward higher requirements. The magnetic field space upward continuation belongs to the system Questions can be obtained by solving the boundary integral equations obtained extension results are very accurate. In mathematics, but the downward continuation is an ill posed problem, not like the upward continuation of the boundary integral equation is obtained as a direct continuation of stable results. Point to the demand for the application of geomagnetic navigation, in order to establish the space geomagnetic database the goal of the geomagnetic field space extension theory is studied, and on the basis of field space extension integral radius on the extension and extension effect results in frequency domain of geomagnetic downward continuation method. The main research achievements and innovations are summarized as follows: (1) introduced the relationship between the geomagnetic field the seven factors and between the composition of the magnetic field and the characteristics of each component of the magnetic field; discusses the extension and extension of the mathematical principle of integral formula for space domain and upward continuation were derived on the basis of Is the frequency domain of the original upward and downward continuation operator; describes the frequency domain field upward and downward extension of the basic flow. (2) studied with magnetic field extension integral radius size of the extension effect on the extension of the unit impulse function, analyzes the different integral radius in the continuation of aeromagnetic data the extension of the contribution rate, the results for the magnetic field upward, downward to provide a reference to determine the extension of integral radius. (3) in the summary of the previous iteration of downward extension method based on the research results, the frequency domain iterative method for the downward continuation of more general promotion, given the frequency domain iterative down the extension of the general formula, and the iterative method to get the downward continuation operator (,) n x yH K K convergence condition, the filtering performance is studied and analyzed. The experimental results show that the frequency domain iteration method for downward continuation operator is essentially 1.5 filter convergence The wave operator, the number of iterations in a certain range, relatively primitive downward continuation operator has a good high-frequency effect, so as to obtain stable extension results, but with the increase of the number of iterations, the iterative operator will be more approximate to the original downward continuation operator, so that the divergence of extended results again change. Therefore, select the appropriate number of iterations is crucial. (4) the principle of nature and regularity of ill posed problem to resolve is studied, a detailed analysis of the frequency domain are currently applied in the field of downward continuation of the downward continuation of Tikhonov regularization method in frequency domain; downward continuation of Tikhonov regularization the transition operator wide band of the improved method, establishes a modified regularization operator; the L curve method is determining the regularization parameter is simplified to construct the auxiliary function to determine the regularization parameter The number of geomagnetic downward space; Tikhonov regularization method developed and improved the use of marine measured data downward continuation regularization method of experimental analysis. The results show that the downward extension of the Tikhonov regularization method and improved regularization method for noise measurement of magnetic data has a strong anti-jamming capability, and improved the downward continuation of the regularization method with Tikhonov regularization method has higher precision of continuation.

【学位授予单位】：山东农业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.2

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